I bike to school in the winter because it's better than standing in the cold waiting for the bus!

It gets down to about -30C + windchill and my tires aren't more than an inch wide--but they salt the roads in this city so it's just slush and not ice on the streets. I can ride on ice, I just prefer not to downhill in traffic.

I wear thermal tights, stretch jeans or short skirt, high warm socks, running shoes (boots with the skirt), thermal long-sleeved shirt, regular long-sleeved shirt, hoodie with the hood up under my helmet (I know, a no-no..), scarf around my mouth and nose, sunglasses to keep the wind off, jacket and gloves under glittens. My biggest concern is frostbite on my fingers, but the commute is less than 5km each way so I can keep them from going numb most of the time.

Unless it's -really- cold (lower than -5) I can go bare-legged under the skirt, but the winter wind is more apt to catch it and offer an unexpected view.

I run in the winter, too. I do shorts down to -5C, tights with reinforced thighs down to -20, and warmup pants over tights lower than that. Toque, scarf around nose and mouth, gloves, thermal long-sleeved shirt and shell. I try to avoid the ice, but snow is excellent conditioning--I'll run in it up to mid-shin.

The only real dangers of winter riding are damaging your lungs, frost-bite to nose/ears/fingers/toes, traffic hazards (skidding vehicles) and ice. If you can manage those (breathe through a scarf, don't skimp on winter wear, only ride on salted streets), no reason not to take to the streets!